Weird shaddows on glossy baked object
Unfortunately, this is not possible.

What you are basically attempting to do is bake reflections, which is the difference between your true render vs. your baked texture version.  

Since this is very environmentally dependant, there is no way to realistically do that in a single image.  The reflections change based on camera angle, room lighting, and other factors can change what the bake should be.  

Note that some game engines manage to fake it, but it needs to be re-baked for every environment, lighting situation, and movement, and falls apart in dynamic scenes.  Blender itself does not support this in any form.